Optical waveguides are commonly used to transmit light from one location to another. One form of optical waveguide is an optical fiber. Optical fibers typically include a core element which has a first refractive index, n.sub.1, and a cladding which has a second refractive index, n.sub.2. The optical fiber transmits light with minimal loss via total internal reflection.
Total internal reflection occurs when the light is incident at the barrier between the core and the cladding with an angle less than a critical angle defined by the difference in refractive index between the core element and the cladding element. The critical angle .theta. is defined by equation (1). EQU .theta.=cos.sup.-1 (n.sub.2 /n.sub.1) (1)
FIG. 1 is a top-plan view of an exemplary optical waveguide formed in an integrated circuit 100 substrate. The integrated circuit substrate 100 has an refractive index n.sub.2 and a light transmitting channel 110 through the substrate has a refractive index n.sub.1. The air surrounding the substrate has a refractive index n.sub.3. To optimally transmit light, the optical waveguide is shaped so that light being transmitted through the channel 110 can not be incident on the edge of the channel 110 at an angle greater than the critical angle. If this were to occur, the light would not be totally internally reflected and, at least some of the light would pass through the wall of the channel 110 and be dissipated in the substrate 100.
To ensure that substantially all of the light which is applied to the input port 120 of the waveguide channel 110 is transmitted through the waveguide and exits the waveguide at the output port 130, the waveguide channel 110 is designed with only gradual bends. Thus, a light ray 112 which comes into the waveguide horizontally, as shown in FIG. 1, is changed to a corresponding vertical ray 118 through a series of reflections 114 and 116. The angle .phi. at which the light ray is incident to the barrier between the channel 112 and the substrate 110 must be less than the critical angle .theta.. Thus, several reflections are needed to produce a total change in the angle of the light ray of 90.degree..
If an optical waveguide routes a light signal on an integrated circuit in any path other than a straight line, the waveguide according to the prior art will need a gradual bend for each change in direction. These gradual bends consume valuable area on the surface of the integrated circuit, area which may otherwise be occupied by signal processing circuitry or other photonic components.